Each species having the ability of reproduction, change and adaptation with the environment can grow in the environment. Due to the alteration of species in the environment, the population distribution of each species may change. The procedure of these changes is investigated by the evolutionary game theory. Rock-Paper-Scissors game is a three-strategy cyclic game in which each strategy dominates another one in a cyclic manner. For example paper dominates rock, but it beats by scissors. In the whole population, species are related to each other. To investigate these relations among the species, the population is modeled by a network. The network is composed of a set of vertices (nodes) in which the relation between vertices and edges is specified. In this thesis, we consider two network structures, namely, two-dimensional square lattice and honeycomb network. The strategies have been randomly and equally distributed in the population. According to the rules of the game, neighboring members are playing with each other. With respect to the results of the simulation which has been carried out with python, a species dominates the whole population. The domination time is considered as an important variable in the analysis of different social and biological populations. Also, this variable is defined as fixation time and the corresponding probability is defined as a fixation probability. According to the results of the conducted research, having (i) a same winning score for three strategies, (ii) different winning scores for three strategies and (iii) same winning scores for two strategies and a bigger winning score for the third strategy, will almost result in a lower fixation time due to the increase of the winning score for the third strategy. Also, having the same winning scores for two strategies and a smaller winning score for the third strategy results in a biger fixation time due to the increase of the winning score for the third strategy. For all the considered conditions, the fixation time of a square lattice is bigger than that of honeycomb network.
